Factorisation of Algebraic Identities

Q.

Factorise the following expression: $7p^2+21q^2$

Q. factorise using suitable identities
p³(q-r)³+q³(r-p)³+r³(p-q)³

Q.

Factorize the expression $x-8x{y}^3$.

Q.

Factorise:
$a^8-2a^4{b}^4+b^8$

1. $\left[\right(a^2-b^2\left)\right(a+b\left)\right(a-b){]}^2$

2. $\left[\right(a^2+b^2\left)\right(a+b\left)\right(a-b){]}^2$

3. $\left[\right(a+b^2\left)\right(a+b\left)\right(a-b){]}^2$

4. $\left[\right(a^2+b\left)\right(a+b\left)\right(a-b){]}^2$

Q. Factors of $(16x^2+4y^2+36z^2+16xy+24yz+48zx)$, are_____.

1. (4x + 2y - 6z)(4x + 2y - 6z)
2. (4x - 2y + 6z)(4x - 2y + 6z)
3. (4x - 2y + 6z)(4x + 2y - 6z)
4. (4x + 2y + 6z)(4x + 2y + 6z)

Q.

Factorise $12xy+25-4x^2-9y^2$.

Q. 9x² - 4 can be factorised as ___.

1. (2x - 3)(2x + 3)
2. (3x - 2 )(3x + 2)
3. (3x + 2)(3x + 2)
4. (2x - 3)(3x + 2)

Q.

Factorise: $a^4-343a$

Q.

Factorise the following using appropriate identities: [4 MARKS]
$1)9x^2+6xy+y^2$
$2)4y^2-4y+1$

Q.

Factorise $a^2-1\frac{9}{16}{b}^2$.

Q.

Expand: ${[\sqrt{3x}-\frac{\sqrt{2}}{5}y]}^2$

1. $3x^2-\frac{2}{5}\sqrt{6x}+\frac{2}{25}$

2. $3x-\frac{2\sqrt{6x}y}{5}+\frac{2}{25}{y}^2$

3. $3x^2-\sqrt{6x}+\frac{4}{25}$

4. $x^2-\frac{2}{5}\sqrt{6x}+\frac{4}{25}$

Q. Factorise:
$81x^3-3y^3$

1. $3(9x-y)[9x^2+3xy+y^2]$
2. $(3x-y)[9x^2+3xy+y^2]$
3. $3(3x-y)[9x^2+6xy+y^2]$
4. $3(3x-y)[9x^2+3xy+y^2]$

Q. Factorise:
$x^3+125$

1. $(x+5)(x^2-5x+25)$
2. $(x+3)(x^2-5x+25)$
3. $(x+5)(x^2-5x+25)$
4. $(x+5)(x^2-10x+25)$

Q.

Factorize: $75(a+b{)}^2-48(a-b{)}^2$.

1. $3(a-9b)(9a-b))$

2. $3(a+3b)(3a+b))$

3. $3(a-9b)(9a+b))$

4. $3(a+9b)(9a+b))$

Q. One of the factors of $(a^2-b^2)(c^2-d^2)-4abcd$ is ______.

1. $(ac-bd+bc+ad)$
2. $(ac+bd+bc-ad)$
3. $(ac-bd+bc-ad)$
4. $(ac+bd+bc+ad)$

Q. $\text{Factorise:}{a}^4+4a^2{b}^2+4b^4$

1. $(a^2+2b^2{)}^2$
2. $(a^2-2b^2{)}^2$
3. $(2a^2+b^2{)}^2$
4. $(2a^2-b^2{)}^2$

Q. $\text{Factorise:}{x}^4-(x-4{)}^4$

1. $16[x-2][x^2-4x+8]$
2. $16[x-2][x^2+4x+8]$
3. $32[x-2][x^2-4x+8]$
4. $16[x+2][x^2-4x+8]$

Q.

Factorize the following expression:

$x^3-x^2+ax+x-a-1$

Q.

Which of the following is/are factor(s) of
$49p^2-36?$

1. $(7p-6)$
2. $(7p+6)$
3. $(5p+6)$
4. $(6p+7)$

Q.

Factorise $169a^4-121b^2$.